Multi-partite quantum nonlocality and Bell-type inequalities in an infinite-order quantum phase transition of the one-dimensional spin-1/2 XXZ chain

Abstract

In this paper, combined with infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multi-partite quantum nonlocality in an infinite one-dimensional quantum spin-1/2 XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, meanwhile only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped anti-ferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order QPT (or Kosterlitz-Thouless QPT) point of the model, the correlation measures always show a local minimum value, regardless of the length of the subchains. It indicates that relatively low hierarchy of multi-partite nonlocality would be observed at the infinite-order QPT point in a Bell-type experiment. The result is in contrast to the existing results of the second-order QPT in the one-dimensional XY model, where multi-partite nonlocality with the hierarchy has been observed. Thus, multi-partite nonlocality provides us an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.

References in corpus (22)

• Area laws for the entanglement entropy - a review
• Efficient classical simulation of slightly entangled quantum computations
• Scaling of Entanglement close to a Quantum Phase Transitions
• Matrix product operator representations
• Bell-type inequalities to detect true n-body non-separability
• Multipartite entanglement in spin chains
• General entanglement scaling laws from time evolution
• Detecting genuine multipartite quantum non-locality -- a simple approach and generalization to arbitrary dimension
• Entanglement and Quantum Phase Transition Revisited
• Entanglement Scaling in the One-Dimensional Hubbard Model at Criticality
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Quantifying multipartite nonlocality
• Testing the Structure of Multipartite Entanglement with Bell Inequalities
• Bell inequalities and entanglement at quantum phase transition in the XXZ Model
• Global quantum correlations in finite-size spin chains
• Hierarchies of multi-partite entanglement
• Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems
• Critical Point Estimation and Long-Range Behavior in the One-Dimensional XY Model Using Thermal Quantum and Total Correlations
• Nonviolation of Bell's Inequality in Translation Invariant Systems
• Long-range multipartite entanglement close to a first order quantum phase transition
• Violation of Bell inequality in perfect translation invariant systems
• Bell-CHSH function approach to quantum phase transitions in matrix product systems

Cited by in corpus (5)

• Magnetic quantum correlation in the 1D transverse-field XXZ model
• Dynamical quantum correlations after sudden quenches
• Quantum Phase Transitions detected by a local probe using Time Correlations and Violations of Leggett-Garg Inequalities
• Violation of the Bell inequality in quantum critical random spin-$1/2$ chains
• Study of quantum non-locality by CHSH function and its extension in disordered fermions